Normalization of input data in Keras

Add BatchNormalization as the first layer and it works as expected, though not exactly like the OP's example. You can see the detailed explanation here.

Both the OP's example and batch normalization use a learned mean and standard deviation of the input data during inference. But the OP's example uses a simple mean that gives every training sample equal weight, while the BatchNormalization layer uses a moving average that gives recently-seen samples more weight than older samples.

Importantly, batch normalization works differently from the OP's example during training. During training, the layer normalizes its output using the mean and standard deviation of the current batch of inputs.

A second distinction is that the OP's code produces an output with a mean of zero and a standard deviation of one. Batch Normalization instead learns a mean and standard deviation for the output that improves the entire network's loss. To get the behavior of the OP's example, Batch Normalization should be initialized with the parameters scale=False and center=False.

Maybe you can use sklearn.preprocessing.StandardScaler to scale you data, This object allow you to save the scaling parameters in an object, Then you can use Mixin types inputs into you model, lets say:

1. Your_model
2. [param1_scaler, param2_scaler]

Here is a link https://www.pyimagesearch.com/2019/02/04/keras-multiple-inputs-and-mixed-data/

https://keras.io/getting-started/functional-api-guide/

There's now a Keras layer for this purpose, Normalization. At time of writing it is in the experimental module, keras.layers.experimental.preprocessing.

https://keras.io/api/layers/preprocessing_layers/core_preprocessing_layers/normalization/

Before you use it, you call the layer's adapt method with the data X you want to derive the scale from (i.e. mean and standard deviation). Once you do this, the scale is fixed (it does not change during training). The scale is then applied to the inputs whenever the model is used (during training and prediction).

from keras.layers.experimental.preprocessing import Normalization

norm_layer = Normalization()
norm_layer.adapt(X)
model = keras.Sequential()
model.add(norm_layer)
# ... Continue as usual.